01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
24.11.1960
E-mail:
,
Keywords:
quasiconformal mappings; mappings with bounded distortion; Beltrami equation; subelliptic equations; geodesic flow; boundary rigidity; ray transform.
Subject:
Systems are classified of partial differential equations whose solution classes are stable in the uniform norm. Properties of solutions are studied for multidimensional analogs of the Beltrami equation describing quasiregular functions of a complex variable. The theory is developed of quasiregular mappings in several spatial variables and a stability theorem is proved for this class. Mappings with bounded distortion on the Heisenberg groups with the Carnot–Caratheodory metric, as well as on more general two-step niltpotent Lie groups, have been defined and studied. Together with C. Croke and V. A. Sharafutdinov, a local boundary rigidity theorem is proved for Riemannian manifolds with above bounded curvature. Together with V. A. Sharafutdinov, a finiteness theorem is proved for infinitesimal isospectral deformations of manifolds whose geodesic flow is of Anosov type, and uniqueness is proved for solutions to some integral geometry problems on these manifolds.
Biography
Graduated from Faculty of Mathematics and Mechanics of Novosibirsk State State University in 1983 (department of mathematical analysis). Ph.D. thesis was defended in 1986. D.Sci. thesis was defended in 1996. A list of my works contains more than 30 titles.
Main publications:
Croke C., Dairbekov N. S., Sharafutdinov V. A. Local boundary rigidity of a compact Riemannian manifold with curvature bounded above // Trans. Amer. Math. Soc. 2000, 352, 3937–3956.
N. S. Dairbekov, O. M. Penkin, D. Savasteev, “Harnack's inequality for harmonic functions on stratified sets”, Sibirsk. Mat. Zh., 64:5 (2023), 971–981
2018
2.
N. S. Dairbekov, O. M. Penkin, L. O. Sarybekova, “An analog of the Sobolev inequality on a stratified set”, Algebra i Analiz, 30:5 (2018), 149–158; St. Petersburg Math. J., 30:5 (2019), 869–875
N. S. Dairbekov, O. M. Penkin, L. O. Sarybekova, “The Poincaré inequality and $p$-connectedness of a stratified set”, Sibirsk. Mat. Zh., 59:6 (2018), 1291–1302; Siberian Math. J., 59:6 (2018), 1024–1033
N. S. Dairbekov, “Stability of mappings with bounded distortion on a Heisenberg group”, Sibirsk. Mat. Zh., 43:2 (2002), 281–294; Siberian Math. J., 43:2 (2002), 223–234
N. S. Dairbekov, “The limit of a sequence of mappings with bounded distortion on the Heisenberg group, and the local homeomorphism theorem”, Sibirsk. Mat. Zh., 41:2 (2000), 316–328; Siberian Math. J., 41:2 (2000), 257–267
N. S. Dairbekov, “On mappings with bounded distortion on the Heisenberg group”, Sibirsk. Mat. Zh., 41:1 (2000), 49–59; Siberian Math. J., 41:1 (2000), 40–48
N. S. Dairbekov, “The morphism property for mappings with bounded distortion on the Heisenberg group”, Sibirsk. Mat. Zh., 40:4 (1999), 811–823; Siberian Math. J., 40:4 (1999), 682–649
N. S. Dairbekov, “On the stability of a class of holomorphic functions in a closed domain”, Sibirsk. Mat. Zh., 38:5 (1997), 1047–1050; Siberian Math. J., 38:5 (1997), 907–909
N. S. Dairbekov, “On the stability of classes of quasiregular mappings of several
space variables”, Dokl. Akad. Nauk, 345:5 (1995), 596–598
12.
N. S. Dairbekov, “Stability of classes of quasiregular mappings in several spatial variables”, Sibirsk. Mat. Zh., 36:1 (1995), 47–59; Siberian Math. J., 36:1 (1995), 43–54
N. S. Dairbekov, “On removable singularities of solutions to first order elliptic systems with irregular coefficients”, Sibirsk. Mat. Zh., 34:1 (1993), 65–69; Siberian Math. J., 34:1 (1993), 55–58
N. S. Dairbekov, “The concept of a quasiregular mapping of several $n$-dimensional
variables”, Dokl. Akad. Nauk, 324:3 (1992), 511–514; Dokl. Math., 45:3 (1992), 578–582
O. L. Bezrukova, N. S. Dairbekov, A. P. Kopylov, “On mappings close in the $C$-norm to classes of solutions of linear elliptic systems of partial differential equations”, Trudy Inst. Mat. Sib. Otd. AN SSSR, 7 (1987), 19–30
18.
N. S. Dairbekov, “On the smoothing of mappings that are close to solutions of first-order elliptic systems”, Sibirsk. Mat. Zh., 28:3 (1987), 70–72; Siberian Math. J., 28:3 (1987), 408–411
N. S. Dairbekov, “On the stability of classes of conformal mappings on a plane and in a space”, Sibirsk. Mat. Zh., 27:5 (1986), 188–191
1985
20.
N. S. Dairbekov, A. P. Kopylov, “$\xi$-stability of classes of mappings, and systems of linear partial differential equations”, Sibirsk. Mat. Zh., 26:2 (1985), 73–90; Siberian Math. J., 26:2 (1985), 216–230
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